Falko Lorenz
Algebra
Volume I: Fields and Galois Theory
Paperback Engels 2005 2006e druk 9780387289304Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.
Specificaties
ISBN13:9780387289304
Taal:Engels
Bindwijze:paperback
Aantal pagina's:296
Uitgever:Springer New York
Druk:2006
Serie:Universitext
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Inhoudsopgave
Constructibility with Ruler and Compass.- Algebraic Extensions.- Simple Extensions.- Fundamentals of Divisibility.- Prime Factorization in Polynomial Rings. Gauss’s Theorem.- Polynomial Splitting Fields.- Separable Extensions.- Galois Extensions.- Finite Fields, Cyclic Groups and Roots of Unity.- Group Actions.- Applications of Galois Theory to Cyclotomic Fields.- Further Steps into Galois Theory.- Norm and Trace.- Binomial Equations.- Solvability of Equations.- Integral Ring Extensions with Applications to Galois Theory.- The Transcendence of ?.- Fundamentals of Transcendental Field Extensions.- Hilbert’s Nullstellensatz.
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